For fully discrete whole life insurances of 1 issued on lives age 50 , the annual net premium, [math]P[/math], was calculated using the following:

(i) [math]\quad q_{50}=0.0048[/math]

(ii) [math]\quad i=0.04[/math]

(iii) [math]\quad A_{51}=0.39788[/math]

A particular life has a first-year mortality rate 10 times the rate used to calculate [math]P[/math]. The mortality rates for all other years are the same as the ones used to calculate [math]P[/math].

Calculate the expected present value of the loss at issue random variable for this life, based on the premium [math]P[/math].

• 0.025
• 0.033
• 0.041
• 0.049
• 0.057

For a fully discrete whole life insurance of 1000 on [math](x)[/math], you are given:

(i) The following expenses are incurred at the beginning of each year:

(ii) An additional expense of 20 is paid when the death benefit is paid

(iii) The gross premium is determined using the equivalence principle

(iv) [math]\quad i=0.06[/math]

(v) [math]\quad \ddot{a}_{x}=12.0[/math]

(vi) [math]{ }^{2} A_{x}=0.14[/math]

Calculate the variance of the loss at issue random variable.

• 14,600
• 33,100
• 51,700
• 70,300
• 88,900

For a fully discrete whole life insurance of 10,000 on (45), you are given:

(i) Commissions are [math]80 \%[/math] of the first year premium and [math]10 \%[/math] of subsequent premiums. There are no other expenses

(ii) Mortality follows the Standard Ultimate Life Table

(iii) [math]i=0.05[/math]

(iv) [math]{ }_{0} L[/math] denotes the loss at issue random variable

(v) If [math]T_{45}=10.5[/math], then [math]{ }_{0} L=4953[/math]

Calculate [math]\mathrm{E}\left[{ }_{0} L\right][/math].

• -580
• -520
• -460
• -400
• -340

For a special fully discrete whole life insurance of 100,000 on (40), you are given:

(i) The annual net premium is [math]P[/math] for years 1 through [math]10,0.5 P[/math] for years 11 through 20, and 0 thereafter

(ii) Mortality follows the Standard Ultimate Life Table

(iii) [math]\quad i=0.05[/math]

Calculate [math]P[/math].

• 850
• 950
• 1050
• 1150
• 1250

For a fully discrete whole life insurance of 1000 on [math](x)[/math] with net premiums payable quarterly, you are given:

(i) [math]\quad i=0.05[/math]

(ii) [math]\quad \ddot{a}_{x}=3.4611[/math]

(iii) [math]\quad P^{(W)}[/math] and [math]P^{(U D D)}[/math] are the annualized net premiums calculated using the 2-term Woolhouse [math](W)[/math] and the uniform distribution of deaths (UDD) assumptions, respectively

Calculate [math]\frac{P^{(U D D)}}{P^{(W)}}[/math].

• 1.000
• 1.002
• 1.004
• 1.006
• 1.008

For a fully discrete 20 -year endowment insurance of 100,000 on (30), you are given:

(i) [math]\quad d=0.05[/math]

(ii) Expenses, payable at the beginning of each year, are:

(iii) The net premium is 2143

Calculate the gross premium using the equivalence principle.

• 2410
• 2530
• 2800
• 3130
• 3280

An insurance company sells special fully discrete two-year endowment insurance policies to smokers (S) and non-smokers (NS) age [math]x[/math]. You are given:

(i) The death benefit is 100,000 ; the maturity benefit is 30,000

(ii) The level annual premium for non-smoker policies is determined by the equivalence principle

(iii) The annual premium for smoker policies is twice the non-smoker annual premium

(iv) [math]\quad \mu_{x+t}^{\mathrm{NS}}=0.1, t\gt0[/math]

(v) [math]\quad q_{x+k}^{\mathrm{s}}=1.5 q_{x+k}^{\mathrm{Ns}}[/math] for [math]k=0,1[/math]

(vi) [math]\quad i=0.08[/math]

Calculate the expected present value of the loss at issue random variable on a smoker policy.

• -30,000
• -29,000
• -28.000
• -27.000
• -26.000

For a 20 -year deferred whole life annuity-due with annual payments of 30,000 on (40), you are given:

(i) The single net premium is refunded without interest at the end of the year of death if death occurs during the deferral period

(ii) Mortality follows the Standard Ultimate Life Table

(iii) [math]\quad i=0.05[/math]

Calculate the single net premium for this annuity.

• 162,000
• 164,000
• 165,200
• 166,400
• 168,800

For a fully discrete whole life insurance of 1 on (50), you are given:

(i) Expenses of 0.20 at the start of the first year and 0.01 at the start of each renewal year are incurred

(ii) Mortality follows the Standard Ultimate Life Table

(iii) [math]\quad i=0.05[/math]

(iv) Gross premiums are determined using the equivalence principle.

Calculate the variance of [math]L_{0}[/math], the gross loss-at-issue random variable.

• 0.023
• 0.028
• 0.033
• 0.0038
• 0.043

For a special fully discrete 3 -year term insurance on (75), you are given:

(i) The death benefit during the first two years is the sum of the net premiums paid without interest

(ii) The death benefit in the third year is 10,000

(iii)

(iv) [math]\quad i=0.04[/math]

Calculate the annual net premium.

• 449
• 459
• 469
• 479
• 489